A Unified Quasi-Particulate Framework for Evolution

Ron Cottam, Willy Ranson, Nils Langloh & Roger Vounckx

In press

Mathematical and Computational Biology:
Computational Morphogenesis, Hierarchical Complexity, and Digital Evolution , p 29.
Edited by C L Nehaniv
Technical Report 97-1-010, The University of Aizu, 1997

Abstract

            The implementation of hierarchical structure in artificial information processing systems ultimately depends on the nature of the rationality underlying system design itself. We propose a new universal paradigm which can extend or replace formal logic, and which is capable of supporting hierarchical evolutionary meta-states and the development of life through "biological" computation.

            In presupposing a coherent universe [1] we acknowledge the correlation of its constituent properties and processes, and accept that all of its regions must remain communicative to support coherence. Distinguishable forms then exist through the actions of one coherent set of processes, and there is no formal distinction between the animate and the inanimate [2]. We find it reasonable that evolution involves not only the development of recognisable entities, but also of the background fields they require to exist [3, 4], and that this coupling will most strongly involve dimensions within which the developing forms themselves are most fragile. The evolutionary co-development of a selectively-dimensioned environment brings with it enhanced computability and competitive advantage. In this scheme, entities can only fulfill their primary criterion of survival by computing sufficiently rapid reactions to external stimuli, and to do so they must have access to simplified internal models of their relationships with the environment. Meta-states characterising these objectivisations correspond to regions of the phase space where its contextual description can be reasonably accurately reduced to a small number of degrees of freedom, and these states are equivalent to limited-parametric provisional stages of an evolutionary computation. All processes are then describable by the relation between their characteristic time scales and those of the contexts to which they must relate, in a way which is analogous to Einsteinian relativity. This description corresponds well to propositions [5] that the critical slowing down associated with phase changes can be attributed to an inability of the constituent media to "compute" sufficiently rapidly their equivalence to the parametric representations implied by the changing states.

            Causality is only possible within a domain exhibiting communicational restriction [6]. We maintain that all entities exist by progressive reduction towards communicational isolation from a common background of diffuse chaotic nonlocality, and that this takes place through hierarchical sets of meta-states of decreasing inter-dimensional diffuseness into perceivable localised forms. Local correlative intercommunication between entities can then be assured by coupling between those meta-states which exhibit only a few degrees of freedom, but universal coherence ultimately demands correlation at and between all meta-state levels right back to the nonlocal causal chaos itself. Transitions of this kind between formal localised order and chaos are naturally asymmetrical, and the necessity of bi-directional "oscillatory" coupling creates an evolutionary time history. This formulation corresponds to describing all natural processes either by a Heisenberg-type uncertainty or by Feynman summation-over-all-paths, and the "fossil record" of such a system corresponds to summation-over-all-histories.

            We believe that scale is a property uniquely to be associated with perceptional systems, and that the presence of scale effects in nature therefore demands recognition of the universe itself as a perceptional system. We propose that perception itself can be treated as a quasi-particle, as can all other (real) localised entities; the prefix "quasi-" then accrues a quantitative sense in the degree of localisation involved. A meta-state depends for its stability not only on control of its context, but also on self-referencing as a means of stabilisation: it must exhibit not only external consciousness but also a degree of self-consciousness. Although the degree of self-consciousness may be variable from a maximum down to zero, there is no freedom to completely eliminate external consciousness; a minimum is imposed by the implications described by objective science; an entity cannot exclude itself from the universe by internal processes. This is an artifact similar to the externally imposed minimum of zero-point energy found in energy-based quantum mechanics: in our description, localisation is equivalent to contextual quantisation, and "physics" is the inanimate "zero-point" ground state of a global quantum system whose higher levels correspond to increasing degrees of "capability for life".

            Implementation of these ideas into a mathematically manipulable scheme depends on the extension of current practice to deal with less-than-deterministic contexts. It is insufficient to resort to classical probability or even fuzzy logic; we must model the natural inter-dimensional diffuseness as a way of characterising the emergence of new models from unfamiliar data. This is evidenced by the difficulties encountered in maintaining logical completeness in the extension of a quantum mechanical treatment to large systems [7]. In a computability-based representation of evolution situated between determinism and chaos, the difference between chance and complicated multi-dimensional determinism becomes blurred, and we must replace classical ideas of probability by a more contextually aware recursive formulation closer to that derived by Dempster and Schafer [8, 9] for discrete sets.

References

[1] Bohm D. Wholeness and the Implicate Order. Routledge & Kegan Paul, London, 1980.

[2] Weber W. Meaning as being in the implicate order philosophy of David Bohm: a conversation. In B. J. Hiley and F. D. Peat, editors, Quantum Implications; p. 440. Routledge & Kegan Paul, London, 1987.

[3] Szamosi G. The Twin Dimensions: Inventing Time and Space. McGraw-Hill, New York, 1986.

[4] Green M. B., Schwarz J. H. & Witten E. Superstring Theory, I; p. 184. Cambridge. U. P., Cambridge, 1987.

[5] see, for example, Gutowitz H. A. & Langton C. G. Mean field theory of the edge of chaos. Proceedings of Third European Conference on Artificial Life. Universidad de Granada, Spain,1995.

[6] Prigogine I. & Stengers I . Order out of Chaos: Man's new dialog with nature; p. 17. Flamingo-Harper Collins, London, 1984.

[7] Antoniou I. Extension of the conventional quantum theory and logic for large systems. In Einstein Meets Magritte, Brussels, Belgium. Vrije Universiteit Brussel, 1995.

[8] Dempster A. P. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics; 38: pp. 325-339, 1967.

[9] Schafer G. A Mathematical Theory of Evidence. Princeton University Press, 1976.
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